IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i1d10.1007_s11009-021-09854-w.html
   My bibliography  Save this article

Uniform Preferential Selection Model for Generating Scale-free Networks

Author

Listed:
  • Raheel Anwar

    (Karl Franzens Universität)

  • Muhammad Irfan Yousuf

    (Member IEEE)

  • Muhammad Abid

    (Pakistan Institute of Engineering and Applied Sciences)

Abstract

It has been observed in real networks that the fraction of nodes P(k) with degree k satisfies the power-law P(k) ∝ k−γ for k > kmin > 0. However, the degree distribution of nodes in these networks before kmin varies slowly to the extent of being uniform as compared to the degree distribution after kmin. Most of the previous studies focus on the degree distribution after kmin and ignore the initial flatness in the distribution of degrees. In this paper, we propose a model that describes the degree distribution for the whole range of k > 0, i.e., before and after kmin. The network evolution is made up of two steps. In the first step, a new node is connected to the network through a preferential attachment method. In the second step, a certain number of edges between the existing nodes are added such that the end nodes of an edge are selected either uniformly or preferentially. The model has a parameter to control the uniform or preferential selection of nodes for creating edges in the network. We perform a comprehensive mathematical analysis of our proposed model in the discrete domain and prove that the model exhibits an asymptotically power-law degree distribution after kmin and a flat-ish distribution before kmin. We also develop an algorithm that guides us in determining the model parameters in order to fit the model output to the node degree distribution of a given real network. Our simulation results show that the degree distributions of the graphs generated by this model match well with those of the real-world graphs.

Suggested Citation

  • Raheel Anwar & Muhammad Irfan Yousuf & Muhammad Abid, 2022. "Uniform Preferential Selection Model for Generating Scale-free Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 449-470, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09854-w
    DOI: 10.1007/s11009-021-09854-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-021-09854-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-021-09854-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Panpan Zhang & Hosam M. Mahmoud, 2020. "On Nodes of Small Degrees and Degree Profile in Preferential Dynamic Attachment Circuits," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 625-645, June.
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emerson, Isaac Arnold & Amala, Arumugam, 2017. "Protein contact maps: A binary depiction of protein 3D structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 782-791.
    2. Faedo, Nicolás & García-Violini, Demián & Ringwood, John V., 2021. "Controlling synchronization in a complex network of nonlinear oscillators via feedback linearisation and H∞-control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Xiao‐Bing Hu & Hang Li & XiaoMei Guo & Pieter H. A. J. M. van Gelder & Peijun Shi, 2019. "Spatial Vulnerability of Network Systems under Spatially Local Hazards," Risk Analysis, John Wiley & Sons, vol. 39(1), pages 162-179, January.
    4. Ruiz Vargas, E. & Mitchell, D.G.V. & Greening, S.G. & Wahl, L.M., 2014. "Topology of whole-brain functional MRI networks: Improving the truncated scale-free model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 151-158.
    5. Igor Belykh & Mateusz Bocian & Alan R. Champneys & Kevin Daley & Russell Jeter & John H. G. Macdonald & Allan McRobie, 2021. "Emergence of the London Millennium Bridge instability without synchronisation," Nature Communications, Nature, vol. 12(1), pages 1-14, December.
    6. Berahmand, Kamal & Bouyer, Asgarali & Samadi, Negin, 2018. "A new centrality measure based on the negative and positive effects of clustering coefficient for identifying influential spreaders in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 41-54.
    7. Zhang, Yun & Liu, Yongguo & Li, Jieting & Zhu, Jiajing & Yang, Changhong & Yang, Wen & Wen, Chuanbiao, 2020. "WOCDA: A whale optimization based community detection algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    8. Soh, Harold & Lim, Sonja & Zhang, Tianyou & Fu, Xiuju & Lee, Gary Kee Khoon & Hung, Terence Gih Guang & Di, Pan & Prakasam, Silvester & Wong, Limsoon, 2010. "Weighted complex network analysis of travel routes on the Singapore public transportation system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5852-5863.
    9. Wang, Qingyun & Duan, Zhisheng & Chen, Guanrong & Feng, Zhaosheng, 2008. "Synchronization in a class of weighted complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5616-5622.
    10. De Montis, Andrea & Ganciu, Amedeo & Cabras, Matteo & Bardi, Antonietta & Mulas, Maurizio, 2019. "Comparative ecological network analysis: An application to Italy," Land Use Policy, Elsevier, vol. 81(C), pages 714-724.
    11. He, He & Yang, Bo & Hu, Xiaoming, 2016. "Exploring community structure in networks by consensus dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 342-353.
    12. T. Botmart & N. Yotha & P. Niamsup & W. Weera, 2017. "Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings," Complexity, Hindawi, vol. 2017, pages 1-18, August.
    13. Sgrignoli, P. & Agliari, E. & Burioni, R. & Schianchi, A., 2015. "Instability and network effects in innovative markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 260-271.
    14. Long Ma & Xiao Han & Zhesi Shen & Wen-Xu Wang & Zengru Di, 2015. "Efficient Reconstruction of Heterogeneous Networks from Time Series via Compressed Sensing," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-12, November.
    15. Wu, Tianyu & Huang, Xia & Chen, Xiangyong & Wang, Jing, 2020. "Sampled-data H∞ exponential synchronization for delayed semi-Markov jump CDNs: A looped-functional approach," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    16. Liang’an Huo & Fan Ding & Chen Liu & Yingying Cheng, 2018. "Dynamical Analysis of Rumor Spreading Model considering Node Activity in Complex Networks," Complexity, Hindawi, vol. 2018, pages 1-10, November.
    17. Yang, Hyeonchae & Jung, Woo-Sung, 2016. "Structural efficiency to manipulate public research institution networks," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 21-32.
    18. Zhu, Mixin & Zhou, Xiaojun, 2023. "Hybrid opportunistic maintenance policy for serial-parallel multi-station manufacturing systems with spare part overlap," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    19. Ye, Dan & Yang, Xiang & Su, Lei, 2017. "Fault-tolerant synchronization control for complex dynamical networks with semi-Markov jump topology," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 36-48.
    20. Dragicevic, Arnaud Z. & Sinclair-Desgagné, Bernard, 2013. "Sustainable network dynamics," Ecological Modelling, Elsevier, vol. 270(C), pages 43-53.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09854-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.